Algebra 1: Common Core (15th Edition)

by
Charles, Randall I.

Published by
Prentice Hall

ISBN 10:
0133281140

ISBN 13:
978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - Chapter Review - Page 537: 42

Answer

$(g-7)(g+2)$

Work Step by Step

To factor a trinomial in the form $g^2+bg+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(g+\_)(g+\_)$.
In the case of $g^2-5g-14$, we are looking for two numbers whose product is $-14$ and whose sum is $-5$. The numbers $-7$ and $2$ meet these criteria because: $$-7\times(2)=-14\;\text{and}\;-7+(2)=-5$$When we insert these numbers into the blanks, we arrive at the factors: $(g-7)(g+2)$.